Teaching calculus today in college

[Tobias Funke]

Troponin, it's nice to read stories like yours and I only wish they were more common.

I don't have any real advice to offer the situation, but it frustrates me deeply to look back at my grammar school years and remember how math was presented to me.

Yeah, it's sad when my 9th graders tell me that their teachers marked them wrong if they left their answer as 3/2 instead of 1 1/2, or how they were forced to write 2+(-3) instead of 2-3, for example. Stuff like this is very common in elementary and middle schools and I'm glad you recovered from it. Good luck!

 

[Troponin]

Troponin, it's nice to read stories like yours and I only wish they were more common.



Yeah, it's sad when my 9th graders tell me that their teachers marked them wrong if they left their answer as 3/2 instead of 1 1/2, or how they were forced to write 2+(-3) instead of 2-3, for example. Stuff like this is very common in elementary and middle schools and I'm glad you recovered from it. Good luck!

Oh yes...my first semester back in school involves a story about that. I went up to my professor and asked a situation similar to that...he looked at me like I was insane. To my relief, he said "it doesn't matter...it's the same number...I don't know what you're asking?!?"

I'm sure he was even more confused when I seemed extremely happy with his non-answer...lol

 

[mbisCool]

When i was younger my teacher marked all of my answers wrong because instead of putting a semi colon between my answer and restriction for what x couldn't equal, i simply put a space...

She also marked me wrong when the end of my square root symbol didnt fully extend over the last number. :/

 

[Troponin]

When i was younger my teacher marked all of my answers wrong because instead of putting a semi colon between my answer and restriction for what x couldn't equal, i simply put a space...

She also marked me wrong when the end of my square root symbol didnt fully extend over the last number. :/

I have a differential equations professor that is FANTASTIC. He doesn't care about ANY of that. He wants you to "understand" what is going on...and almost prefers you to not follow the "plug and chug" list of operations for each type of solution.
He's a very difficult professor so a lot of students seem to really dislike him, but I absolutely love him.

All the arbitrary accounting style order and rules that I've always felt had more to do with memorization than understanding the materials are considered just that...arbitrary memorization that doesn't prove if you understand the material.

 

[descendency]

What are some ideas on how to improve this?

More abstinence from people who shouldn't be parents!

By the time you get these students in Calculus I, you have gotten a student who has developed years of **** poor mathematics. I can't say I was a great mathematician taking calculus I, but I can say I knew what the basic terminology was.

Knowing what a plane, a denominator, and other very simple concepts are is fundamental to have any hope of passing calculus.

Unfortunately, teaching fundamentals and refusing to work with students who won't meet you on a fundamentals level is the only hope you have.

If they don't understand what a number line means how will they understand a delta-epsilon proof? or a limit? or handedness? or derivatives? or integrals? or techniques of integration? or optimization? or applications of integration? or anything else?

edit: As for marking off points for sloppy work, you deserve them. When an instructor sets out a standard, you deserve points off for not being able to follow a standard. Half-***ing it is just not acceptable nor should it be. Not drawing a division bar long enough shows how little you care for the work you are doing. You feel your time is being wasted. If that's the case, don't waste your instructors time with your test/homework.

If the instructor themself can not follow a standard though, then you have a gripe. However, drawing arrowheads on your graph to indicate direction of increasing is not too much to ask. Or labeling the axes.

 

[uman]

I would consider it unreasonable that a teacher would mark off for using a semicolon instead of a space.

 

[Tobias Funke]

Teachers should only set reasonable standards. What if a teacher wanted you to write a...@b instead of a+b for the semester? Sure it's an extreme example, but it's no more silly than requiring 1.5 instead of 3/2 (unless the point of the exercise is to get practice with decimals). Descendency, it seems like you're thinking of something like the difference between $$\sqrt{a}b$$ and $$\sqrt{ab}$$, which definitely deserves some correcting. I'm talking about much more trivial things.

Also note that these experiences all seem to stop in college. Professors aren't going to care if you write $$A-B$$ or $$A\setminus B$$, but too many 1-12 teachers would and it's just plain stupid sometimes.

Actually I guess the equivalent in college would be those annoying computer homework sites that only accept the answer in a certain form that doesn't seem to be any better or neater than your own. Luckily I've never had to use them, but I tried helping a friend of mine and was very frustrated.

I feel like ending this on a positive note though. Today one of my students got a 100 on a math test for the first time in a year, and another student said "this is actually kinda fun once you get it" about solving systems of equations! That just makes the day so much better

 

[qwerty2x]

We had our year 12 end of year exam for specialist math(for the whole state) and we were allowed to bring in a bound reference. Everyone came in holding a large book with LOTS of papers glued into it that had problems and questions with the working out, while i came in with a lousy one-paged A4 sheet of paper with almost nothing on it as i didnt know what to write on it(its a math exam what am i suppose to put on it??).
Anyway the exam started and I am doing the problems, i look up and i see people flicking through their papers "trying to find a similar question" to what was being asked.

I ended up getting the highest in the class and in the top 7% of the state, i guess the way the other students learn the material is really the problem these days(mind you their parents are payed **** loads for private tutiton).

would you say that the rate of drop-outs for engineering students in higher than that of most other disiplines?

 

[symbolipoint]

qwerty2x, you made a nice observation about test-taking and possibly study methods, and then after that, you made a statement which seems unrelated. Readers may have clearer responses or comments if you would show a transition to that last statement.

One reason ignoring quantity for why any university or college student would drop from their formal education is to work, do an employed job, or start a business. You are probably trying to address something opposite to that. Engineering may be difficult to study well. Students might drop because they need to work to earn money/more money, or change major field due to difficulty of coursework, or drop intending to return but never do (but possibly work for many years after dropping from Engineering study).

YOU might be either more talented than the other test takers, or you have better study methods than they, or you may have studied longer and harder than they. Good Work!

EDIT: How much did this test involve Calculus? Could you tell us which topics from Calculus were in the test's content? Did the test rely on multiple choice answers, were showing written steps a main feature of your responses to the questions? Were proofs involved? Were essays involved? These are useful questions in this thread-topic since this could relate to the title, "teaching calculus today in college".

 

[qwerty2x]

the exam was made up of 22 multiple choice questions and 5 extended answer question.
Here is a link to part 2 of the exam(cant find part 1)(not uploaded by me).

http://trinon.info/exams/VCAA_2008_Specialist_Mathematics_Exam_2.pdf

EDIT:yeh sorry that statement does sound unrelated, just wanted to get a feel of the difficulty of engineering at uni.

 

[buffordboy23]

the exam was made up of 22 multiple choice questions and 5 extended answer question.

There are many questions on that test (particularly complex variables and differential equations) for which my high school education would not have prepared me. And, I was an accelerated mathematics student in my school, which was a very small school in a somewhat rural setting.

Who takes this test? Where is it administered? What is its purpose?

 

[qwerty2x]

There are many questions on that test (particularly complex variables and differential equations) for which my high school education would not have prepared me. And, I was an accelerated mathematics student in my school, which was a very small school in a somewhat rural setting.

Who takes this test? Where is it administered? What is its purpose?

Every year 12 student that takes the subject in victoria(approx 6000 people i think, small compared to other subjects) take this subject, it is like advanced math and i think its the second hardest math that a year 12 can take in victoria. administrators are VCAA.

Part 1 of the exam was much harder even tho it was only 10 questions.

 

[kbaumen]

I feel like ending this on a positive note though. Today one of my students got a 100 on a math test for the first time in a year, and another student said "this is actually kinda fun once you get it" about solving systems of equations! That just makes the day so much better

I definitely agree to the last sentence. Of course, I'm not a teacher, just a 12th grader but sometimes (quite often actually) I help other students from my class and it really feels nice to hear them say "wow, now that you explain, it seems quite interesting, hey if I substitute this with that, you get this and that's how you prove that, so this is another application of that, wow..." I can imagine, that being a teacher even if 99 of your students think that you suck as much as the subject does, it's still worth sucking it up if later you get a "thanks a lot, this is very interesting" from one student.

 

[Moonbear]

Teachers should only set reasonable standards. What if a teacher wanted you to write a...@b instead of a+b for the semester? Sure it's an extreme example, but it's no more silly than requiring 1.5 instead of 3/2 (unless the point of the exercise is to get practice with decimals).

In elementary school, when they make you do exercises like that, it is indeed the objective of the exercise to practice manipulating fractions or converting fractions to decimal points. It's not just a teacher being nitpicky, it's a teacher trying to ensure the students have the fundamentals correct. Part of that is making sure a student understands that 3/2 is the same as 1 1/2 and isn't confusing it with 2/3. When learning fractions, confusing the numerator and denominator is commonplace, so forcing students to do added steps that demonstrate they comprehend the distinction is necessary. The point of homework and exams is for the student to demonstrate they have mastered whatever topic they are learning, not that they have provided some reasonable semblance of an effort enough to get away with others guessing what they are thinking. And, when so many mistakes in math happen because of carelessness and sloppy handwriting, it's good for teachers to enforce those rules early so students develop careful habits for when the math gets harder. It's the same reason teachers grade notebooks; it makes students develop good habits.

 

[maze]

But it also causes kids to feel like math is nothing more than pedantic manipulation of symbols according to arbitrary rules. This couldn't be further from the truth, and it directly contributes to the dislike of math by the general population.

 

[buffordboy23]

But it also causes kids to feel like math is nothing more than pedantic manipulation of symbols according to arbitrary rules. This couldn't be further from the truth, and it directly contributes to the dislike of math by the general population.

Are you suggesting that making students accountable for the quality of their work and meeting teacher expectations is the reason for the dislike of math?

In adding to what Moonbear and Tobias Funke stated previously, I think the most important question to ask regarding this matter is, "Does such and such requirement align well with the lesson or overall course objectives?" For third or fourth graders, requiring them to carry out each step when it comes to fractions is acceptable in my opinion for the reasons Moonbear mentioned. But for a typical eighth grader, forget about it since this skill should have already been obtained.

I agree with what you said on why math is disliked by the general population: it's nothing more than pedantic manipulation of symbols according to arbitrary rules (and a nice catchy mnemonic tune every now and then). I think the fundamental and underlying reason for this is the teacher and the methods of instruction employed. Usually, these instructional methods are simply the pedantic manipulation of symbols.

 

[vsheng]

I am a student in university, recently i am facing problem to deal with my calculus lecturer,
well, actually they are certain similar point with your problem with the problem between me and my lecturer...

"Many never ask questions, and those who do, often ask things that could be found immediately by looking them up in the index of the book. "

Most of my friend do not ask question because they can't even understand what the lecturer talking about, for those understand who are able to ask question, they are often in a ;hald understand' condition, when they are in that condition, don't expect them to think normally as a normal person.


"Questions more often focus on "what will be tested?" instead of how to understand what has been taught."

Every student are worry and emphasing the result of their academic, if not, they are not actually concern about their future..

"Everyone seems to have taken calculus in high school, but most also seem not to know anything about algebra or geometry or trigonometry. With the advent of calculators some also do not know simple arithmetic, like how to multiply two digit numerals. (I have had students who had to add up a column of thirteen 65's on a test, apparently not knowing how to multiply 13 by 65.)
Many think that having taken a subject "2 years ago" is a valid excuse to have forgotten the material, and to expect the teacher to reteach the prerequisites. Appparently no one ever dreams of reviewing the prerequisites before the course starts. Books like "Calculus for cretins" are apparently more popular than books like "Calculus for science majors"."

Student have to take a lot of subject beside calculus, and they have to join activities too,
further more, as a student, when they are in holiday, many of them will just let their mind relax in a this short period,and they of sourse, they do not study the previous subjest that they have taken...so, sometimes if they forgot some important steps, it does not show that they are not a good student...

 

[Tobias Funke]

snip

I agree with you since you were specifically talking about elementary school. But what I'm seeing with my high school freshmen isn't comprehension and easy conversion between number representations. They're just confused. They didn't seem to understand that 22/5 is a number and they insisted on changing it to 4 2/5 or even wasting time doing the long division. Their previous teachers have forced them to write fractions in a certain way and it was hard for them to change. Like maze said, I'm telling them one thing in opposition to their middle school teachers, probably leaving them to stop thinking about the subject and just following my orders.

They're improving their abilities to memorize facts which to them are meaningless and regurgitating on their quizzes. That's not the kind of teaching I had in mind and I'm not sure I'm qualified to teach the low level math that they need. I chose high school for a reason, after all. Next year I'm going to ask to separate the students in the first week or so into algebra 1 and pre-algebra. Whether they officially do so or not, if I teach the same class next year it's going to be a reintroduction to fractions, half eaten pies and all, for about 3 months.